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Weighted Interpolation: the L∞ Theory. I

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Abstract

In this paper we deal with weighted interpolation on the real line. We show that the Hermite-Fejér interpolation process is not optimal, but the Grünwald operator is the ideal case.

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References

  1. Z. Ditzian and D. S. Lubinsky, Jackson and smoothness theorems for Freud weights in L p (0 < p ≦ ∞), Constr. Approx., 13 (1997), 99–152.

    Google Scholar 

  2. G. Freud, Orthogonal Polynomials, Pergamon Press/Akadémiai Kiadó (Budapest, 1970).

    Google Scholar 

  3. G. Criscuolo, B. Della Vecchia, D. S. Lubinsky and G. Mastroianni, Functions of the second kind for Freud weights and series expansions of Hilbert transforms, J. Math. Anal. and Appl., 189 (1995), 256–296.

    Google Scholar 

  4. G. Grünwald, On the theory of interpolation, Acta Math., 75 (1942), 219–245.

    Google Scholar 

  5. A. L. Levin and D. S. Lubinsky, Christoffel functions, orthogonal polynomials and Nevai's conjecture for Freud weights, Constr. Approx., 8 (1992), 463–535.

    Google Scholar 

  6. D. S. Lubinsky, Hermite and Hermite-Fejér interpolation and associated product integration rules on the real line: The L theory, J. Approx. Theory, 70 (1992), 284–334.

    Google Scholar 

  7. D. S. Lubinsky and P. Rabinowitz, Hermite and Hermite-Fejér interpolation and associated product integration rules on the real line: The L 1 theory, Can. J. Math., 44 (1992), 561–590.

    Google Scholar 

  8. H. N. Mhaskar, Bounds for certain Freud-type orthogonal polynomials, J. Approx. Theory, 63 (1990), 238–254.

    Google Scholar 

  9. H. N. Mhaskar and E. B. Saff, Where does the sup-norm of a weighted polynomial live?, Constr. Approx., 1 (1985), 71–91.

    Google Scholar 

  10. H. N. Mhaskar and Y. Xu, Hermite interpolation at the zeros of certain Freud-type orthogonal polynomials, Acta Math. Hungar., 60 (1992), 225–240.

    Google Scholar 

  11. J. Szabados, Weighted Lagrange and Hermite—Fejér interpolation on the real line, J. of Inequalities and Applications, 1 (1997), 99–123.

    Google Scholar 

  12. V. E. S. Szabó, Weighted interpolation: The L theory II, manuscript.

  13. á. P. Horváth, p(w)-normal point system, Acta Math. Hungar., to appear.

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Szabó, V.E.S. Weighted Interpolation: the L∞ Theory. I. Acta Mathematica Hungarica 83, 131–159 (1999). https://doi.org/10.1023/A:1006675822213

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